Fractional calculus in analysis, dynamics, and optimal control
This book is devoted to applications of fractional calculus in classical fields of mathematics like analysis, dynamics, partial differential equations and optimal control. The first chapter deals with the notion of local fractional derivatives and its applications to the study of regularity and geometry of curves. The second chapter develops the notion of fractional embedding and fractional assymetric calculus of variations in order to find fractional Lagrangian variational structures for class…
Read More ↓Title Statements
- Full title :Fractional calculus in analysis, dynamics, and optimal control / Jacky Cresson, editor.
Summary
This book is devoted to applications of fractional calculus in classical fields of mathematics like analysis, dynamics, partial differential equations and optimal control. The first chapter deals with the notion of local fractional derivatives and its applications to the study of regularity and geometry of curves. The second chapter develops the notion of fractional embedding and fractional assymetric calculus of variations in order to find fractional Lagrangian variational structures for classical dissipative partial differential equations. In continuation of this chapter, a fractional analog.
Read More ↓Edition Statements
- Publication Date:2014
Publication Statements
- Publisher(s):Nova Publishers
- Place of Publication:New York
- Language:eng
- Publication Date:2014
The Physical Object
- Description:1 online resource.
Edition Identifiers
- ISBN:9781629486598, 1629486590
- oclc:on1162537691
- LC Classification:QA314
- Dewey Decimal:515/.83
Table of Contents
""FRACTIONAL CALCULUS IN ANALYSIS, DYNAMICS AND OPTIMAL CONTROL""; ""FRACTIONAL CALCULUS IN ANALYSIS, DYNAMICS AND OPTIMAL CONTROL""; ""LIBRARY OF CONGRESS CATALOGING-IN-PUBLICATION DATA""; ""CONTENTS""; ""PREFACE""; ""Chapter 1: LOCAL FRACTIONAL DERIVATIVES""; ""1. Introduction""; ""2. Non-differentiable and Non-analytic Functions""; ""3. Measure and Dimension""; ""4. Fractional Calculus""; ""5. Generalizations""; ""Acknowledgment""; ""References""; ""Chapter 2: FRACTIONAL VARIATIONAL EMBEDDING AND LAGRANGIAN FORMULATIONS OF DISSIPATIVE PARTIAL DIFFERENTIAL EQUATIONS""; ""1. Introduction""
""2. Variational Principles and Dissipative Systems""""3. Embeddings Formalisms of ODEs and PDEs""; ""4. Asymmetric Fractional Embedding""; ""5. Fractional Variational Formulation of Dissipative Ordinary Differential Equations""; ""6. Variational Formulation of Dissipative Partial Differential Equations""; ""References""; ""Chapter 3: A CLASS OF FRACTIONAL OPTIMAL CONTROL PROBLEMS AND FRACTIONAL PONTRYAGIN�S SYSTEMS. VARIATIONAL INTEGRATOR AND EXISTENCE OF CONTINUOUS/DISCRETE NOETHER�S THEOREMS""; ""Introduction""; ""1. A Class of Fractional Optimal Control Problems""
""2. Variational Int…
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